Embeddings into \(\mathbb{B}\)-Cyclic Banach Spaces

Tasoev, B. B.
Vladikavkaz Mathematical Journal 2022. Vol. 24. Issue 4.

Abstract:
For a complete Boolean algebra \(\mathbb{B}\) and nonzero \(\pi\in \mathbb{B}\), the notion of an \(\mathbb{B}_{\pi}\)-embedding of Banach spaces into \(\mathbb{B}\)-cyclic Banach spaces is introduced. The notion of a lattice  \(\mathbb{B}_{\pi}\)-embedding of Banach lattices into \(\mathbb{B}\)-cyclic Banach lattices is also introduced. A criterion for the \(\mathbb{B}_{\pi}\)-embedding of a space  of continuous vector-valued functions with values  in an arbitrary Banach space into a \(\mathbb{B}\)-cyclic Banach space is established, as well as a criterion for the lattice  \(\mathbb{B}_{\pi}\)-embedding of a space of continuous vector-valued functions with values  in an arbitrary Banach lattice into a \(\mathbb{B}\)-cyclic Banach lattice. The  obtained results allow us to outline an approach for isometric and isomorphic classification of  \(\mathbb{B}\)-cyclic Banach spaces. In the course of establishing the results, the tool of lattice-valued spaces was widely used.

Keywords: Banach lattice, \(\mathbb{B}\)-cyclic Banach space, isomorphic classification

+ References

The sole copyright holder of the published work is the Founder of the Vladikavkaz Mathematical Journal. The terms of use of this work are governed by an open license (Creative Commons Attribution-NonCommercial 4.0 International). The use of metadata of the scientific article, including the title, abstract, author information, references, identifiers, and other bibliographic description elements for subsequent unrestricted use, is carried out under the terms of the CC BY or CC0 open licenses.